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This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…

Analysis of PDEs · Mathematics 2017-09-26 Xiaoxu Xu , Bo Zhang , Haiwen Zhang

It is proved that a general polyhedral perfect conducting obstacle in $\mathbb{R}^3$, possibly consisting of finitely many solid polyhedra, is uniquely determined by the far-field pattern corresponding to a single incident wave. This…

Analysis of PDEs · Mathematics 2009-11-13 Hongyu Liu

We consider a unique continuation problem for the wave equation given data in a volumetric subset of the space time domain. In the absence of data on the lateral boundary of the space-time cylinder we prove that the solution can be…

Numerical Analysis · Mathematics 2025-10-24 Erik Burman , Lauri Oksanen , Janosch Preuss , Ziyao Zhao

We prove sharp wavenumber-explicit error bounds for first- or second-family-N\'ed\'elec-element (a.k.a. edge-element) conforming discretisations, of arbitrary (fixed) order, of the variable-coefficient time-harmonic Maxwell equations posed…

Numerical Analysis · Mathematics 2026-01-09 Théophile Chaumont-Frelet , Jeffrey Galkowski , Euan A. Spence

This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent…

Analysis of PDEs · Mathematics 2021-09-23 Yanli Chen , Peijun Li , Xu Wang

Inverse scattering problem is discussed for the Maxwell's equations. A reduction of the Maxwell's system to a new Fredholm second-kind integral equation with a {\it scalar weakly singular kernel} is given for electromagnetic (EM) wave…

Analysis of PDEs · Mathematics 2012-06-27 A. G. Ramm

The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell…

Analysis of PDEs · Mathematics 2023-06-09 Masaru Ikehata

This paper is concerned with the unique identification of the shape of a scatterer through a single far-field pattern in an inverse elastic medium scattering problem with a generalized transmission boundary condition. The uniqueness issue…

Analysis of PDEs · Mathematics 2023-12-06 Huaian Diao , Ruixiang Tang , Hongyu Liu , Jiexin Tang

This paper investigates the inverse scattering problem for the magnetic Schr\"odinger equation. We first establish the well-posedness of the direct problem through a variational approach under physically meaningful assumptions on the…

Analysis of PDEs · Mathematics 2025-10-10 Chaohua Duan , Zhen Xue

We consider an inverse boundary value problem for Maxwell's equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric…

Analysis of PDEs · Mathematics 2018-07-11 Monika Pichler

In this paper we prove strong unique continuation principle and unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open domain. Our proofs are based on the…

Analysis of PDEs · Mathematics 2018-09-26 Veronica Felli , Alberto Ferrero

This paper considers the time-harmonic Maxwell equations with impedance boundary condition.We present $H^2$-norm bound and other high-order norm bounds for strong solutions. The $H^2$-estimate have been derived in [M. Dauge, M. Costabel and…

Analysis of PDEs · Mathematics 2018-04-24 Peipei Lu , Yun Wang , Xuejun Xu

We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 Y. V. Fyodorov , D. V. Savin , H. -J. Sommers

In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic…

Analysis of PDEs · Mathematics 2020-10-19 Anne-Sophie Bonnet-Ben Dhia , Lucas Chesnel , Mahran Rihani

This paper treats the time-harmonic electro-magnetic scattering or radiation problem governed by Maxwell's equations in an exterior weak Lipschitz domain divided into two disjoint weak Lipschitz parts We will present a solution theory using…

Analysis of PDEs · Mathematics 2019-04-30 Frank Osterbrink , Dirk Pauly

In this paper, we study the stability of the inverse conductivity problem of determining a convex polyhedral inclusion embedded in a homogeneous isotropic medium from a single boundary measurement. The main tools in our analysis are…

Analysis of PDEs · Mathematics 2026-05-19 Chun-Hsiang Tsou

We analyze the conforming approximation of the time-harmonic Maxwell's equations using N\'ed\'elec (edge) finite elements. We prove that the approximation is asymptotically optimal, i.e., the approximation error in the energy norm is…

Numerical Analysis · Mathematics 2023-09-26 T. Chaumont-Frelet , A. Ern

We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these…

Analysis of PDEs · Mathematics 2019-03-11 Pedro Caro , Ru-Yu Lai , Yi-Hsuan Lin , Ting Zhou

A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…

Computational Physics · Physics 2020-02-18 Johan Helsing , Anders Karlsson

To design a uniaxial anisotropic metamaterial a layered cylindrical metamaterial is introduced for TE polarization. Unlike to the previous work, which the layers were in radial direction, here the layers are in azimuthal direction.…

Optics · Physics 2017-10-11 M. R. Forouzeshfard , Masoud Mohebbi , Aliyeh Mollaei